We show that if an exponential polynomial \(\sum _{i=1}^m P_i(z)e^{Q_i(z)}\), where \(P_i\), \(Q_i\in \mathbb C[z]\), is a dth power, \(d\ge 2\), of an entire function g, then g itself is also an exponential polynomial. We also study when a multivariable polynomial with moving targets of slow growth evaluated at unit arguments can be a dth power of an entire function. Finally, we formulate a boundary case of the Green–Griffiths–Lang conjecture for projective spaces with moving targets.

中文翻译：

---

关于格林-格里菲斯-朗猜想的指数多项式的d根及相关问题

我们证明，如果指数多项式\（\ sum _ {i = 1} ^ m P_i（z）e ^ {Q_i（z）} \），其中\（P_i \），\（Q_i \在\ mathbb C [ z] \）是整个函数g的d次方\（d \ ge 2 \），则g本身也是指数多项式。我们还研究了以单位论元评估的具有缓慢增长的移动目标的多元多项式何时可以作为整个函数的d次方。最后，我们为具有移动目标的投影空间制定了Green–Griffiths–Lang猜想的边界案例。